A History of Mathematics: From Mesopotamia to Modernity

A History of Mathematics: From Mesopotamia to Modernity

A History of Mathematics: From Mesopotamia to Modernity

Synopsis

A History of Mathematics covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwasizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

Excerpt

This book has its origin in notes which I compiled for a course on the history of mathematics at King's College London, taught for many years before we parted company. My major change in outlook (which is responsible for its form) dates back to a day ten years ago at the University of Warwick, when I was comparing notes on teaching with the late David Fowler. He explained his own history of mathematics course to me; as one might expect, it was detailed, scholarly, and encouraged students to do research of their own, particularly on the Greeks. I told him that I gave what I hoped was a critical account of the whole history of mathematics in a series of lectures, trying to go beyond what they would find in a textbook. David was scornful. 'What', he said, 'do you mean that you stand up in front of those students and tell stories?'I had to acknowledge that I did.

David's approach meant that students should be taught from the start not to accept any story at face value, and to be interested in questions rather than narrative. It's certainly desirable as regards the Greeks, and it's a good approach in general, even if it may sometimes seem too difficult and too purist. I hope he would not be too hard on my attempts at a compromise. The aims of the book in this, its ultimate form, are set out in the introduction; briefly, I hope to introduce students to the history, or histories of mathematics as constructions which we make to explain the texts which we have, and to relate them to our own ideas. Such constructions are often controversial, and always provisional; but that is the nature of history.

The original impulse to write came from David Robinson, my collaborator on the course at King's, who suggested (unsuccessfully) that I should turn my course notes into a book; and providentially from Alison Jones of the Oxford University Press, who turned up at King's when I was at a loose end and asked if I had a book to publish. I produced a proposal; she persuaded the press to accept it and kept me writing. Without her constant feedback and involvement it would never have been completed.

I am grateful to a number of friends for advice and encouragement. Jeremy Gray read an early draft and promoted the project as a referee; the reader is indebted to him for the presence of exercises. Geoffrey Lloyd gave expert advice on the Greeks; I am grateful for all of it, even if I only paid attention to some. John Cairns, Felix Pirani and Gervase Fletcher read parts of the manuscript and made helpful comments; various friends and relations, most particularly Jack Goody, John Hope, Jessica Hines and Sam and Joe Gold Hodgkin expressed a wish to see the finished product.

Finally, I'm deeply grateful to my wife Jean who has supported the project patiently through writing and revision. To her, and to my father Thomas who I hope would have approved, this book is dedicated.